December 4, 2012
RMO 2012 solution to Question No. 6
6. Find all positive integers n such that is a perfect square.
We use the fact that between square of two consecutive numbers there exist no perfect square. That is between
there is no square.
are two consecutive perfect square and
is always a number between them for n > 2 (easily proved by induction).
Hence the only solution is n = 2.
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